Various schemes have been proposed for evaluating physical parameters of a semiconductor. In one example disclosed in U.S. Pat. No. 4,854,710, information is derived by analyzing the interaction between sample features and an electron-hole plasma induced in the sample. Variations in plasma density, which is in part a function of variations in the sample, are measured based on the effect of the plasma on the refractive index at the surface of the sample. A radiation probe is reflected off the surface of the sample and changes induced in the refractive index are monitored to obtain information about surface and subsurface characteristics of the sample.
The patentees in U.S. Pat. No. 4,854,710 state that their invention can be used for microscopically evaluating ion dopant concentrations in a semiconductor by measuring changes in reflectivity of a probe beam. A periodic energy beam is used to infuse energy into the sample and create an electron-hole plasma. The diffusion profile or changing density of the plasma is detected at the sample surface through the use of the probe beam. The changing output signals of the detected, reflected probe beam which are in phase with the energy beam can be plotted to indicate variations in dopant or defect concentrations. These output signals are compared to predetermined reflectivity measurements made on a known reference sample. The latter information can be stored in a processor and compared to give relative information concerning the tested sample.
U.S. Pat. No. 5,883,518 discloses a doping level measuring system which may be used to control a semiconductor fabrication process. In the measuring system a detector detects the phase shift of an analyzer beam relative to a reference beam, and the doping level in a preselected doped region is determined from the phase shift. The phase shift of an analyzer beam is also detected in a method disclosed in U.S. Pat. No. 5,966,019, which employs both an analyzer beam and a generation beam. A property of a semiconductor substrate is calculated from the detected phase shift.
U.S. Pat. No. 6,049,220 discloses an apparatus and method for evaluating a wafer of semiconductor material which use diffusive modulation (without generating a wave of carriers) for measuring a material property (such as any one or more of mobility, doping, and lifetime) that is used in evaluating a semiconductor wafer. The measurements are based on measurement of reflectance, for example, as a function of carrier concentration. In one implementation, the semiconductor wafer is illuminated with two beams, one with photon energy above the band gap energy of the semiconductor, and another with photon energy near or below the band gap. An attribute, derived from measurements on the wafer is interpolated with respect to corresponding attributes of wafers having a known material property (or process condition) to determine a corresponding property or condition of the wafer under measurement.
The Cauchy empirical model is the basis for modeling at least one physical parameter of a film for a wide variety of materials. Cauchy modeling can predict the experimental results in the long wavelength range where such optical transitions as band-to-band and band-to-interband state transitions do not occur. For example, Cauchy modeling can be used to fit the reflectance and ellipsometric measurement data of organic arc material for wavelengths longer than about 450 nm. However, data from measurements with light in the ultraviolet wavelength range do not match up well with the data predicted by the Cauchy model. There is a need for an improved model and method of calculating at least one parameter of a film using the model, which can accurately simulate or model the characteristic of a material for measurements over a wide range of wavelengths, including those in the ultraviolet wavelength range. An accurate model and method suitable for use with semiconductor materials and dielectrics having varying concentrations of interband states in the material would also be beneficial.
To this end, the improved method of the present invention for calculating at least one physical parameter of a film comprises relating at least one physical parameter to scattering caused by interband states. This relating includes using a theoretical model which includes a quantum mechanical transition equation for transitions between valence and/or conduction bands and interband states of the material. The method can be used for calculating the refractive index and the extinction coefficient of the film. It is applicable for semiconductor and dielectric film materials having varying levels of interband states. Apparatus for producing and monitoring films having at least one desired physical parameter, which employ the method are also provided.
These and other features and advantages of the present invention will become more apparent from the following description when taken in connection with the accompanying drawings which show, for purposes of illustration only, several example embodiments in accordance with the present invention.